Abstract
This paper extends previously proposed bound propagation algorithm [11] for computing lower and upper bounds on posterior marginals in Bayesian networks. We improve the bound propagation scheme by taking advantage of the directionality in Bayesian networks and applying the notion of relevant subnetwork. We also propose an approximation scheme for the linear optimization subproblems. We demonstrate empirically that while the resulting bounds loose some precision, we achieve 10-100 times speedup compared to original bound propagation using a simplex solver.